Fluorescence, mental disturbance, dancing. The Effect has some of the ingredients that made The Curious Incident of the Dog in the Night-Time such a hit in the same theatre. There is a smidgen of formula about Rupert Goold's effective production, but that is dispelled by Lucy Prebble's incisive dialogue. It is extraordinary that a condition characterised by withdrawal of energy should make such a dynamic piece of theatre.

Prebble's play is about depression. It is also about its opposite: falling in love. She asks, through four characters – two non-depressive volunteers in a drug trial and two doctors, one a depressive – not only what treatments may work ("the history of medicine is the history of placebos") but, more fundamentally, what counts as psychiatric illness? When people are bereaved, distraught, estranged from their usual selves, should they be treated as if they are unwell? And if they are hyper-happy, should that be cured too?

Prebble really researches and the range of her subjects suggests she will have a long theatrical life. Her first play, The Sugar Syndrome, was a shrewd study of phobia and obsession. The galvanic Enron – also directed by Goold – lit up the financial crisis. The Effect was inspired by 2006 drug trials at Northwick Park hospital in London, which resulted in volunteers suffering organ failure: it features some sloshing around of brains in buckets and a certain amount of holding them, Hamlet-style, aloft. The only notable inaccuracy seems to be that brain surgery is not, as the play suggests, smelly.

Prebble has said that she wrote The Effect for Billie Piper, after they had worked together on television's Secret Diary of a Call Girl. It is a lovely collaboration. Piper, as close to some spectators as she might be on TV, is both detailed and dramatic. Her face looks as if something – tears or an enormous chuckle, perhaps a whole different Billie Piper – were trapped inside it and about to burst out; sometimes it does. She is well matched by the casually clever Jonjo O'Neill who, in a dance especially created for him, proves able to tap his way all over the stage. Around them circle Tom Goodman-Hill, utterly persuasive as a puffed-up practitioner convinced that depression can be nailed with chemicals, and Anastasia Hille, his ex-lover and a depressive. It is extraordinary when Hille speaks of people with one skin missing; there has never been an actress more able to suggest that the audience is X-raying her.

Some pain is cocooned by Sarah Angliss's music – electronic dongs of the kind that madden while they are supposed to soothe – but Miriam Buether's design ensures that those in the front rows are implicated: audience members sit next to glossy tables with huge vases of stiff flowers. The Effect also contains the theatrical accessory of the season. Alan Bennett's Peoplefeatured celebrity urine. This time it is just ordinary wee.

Just when the flurry of Chekhov revivals seemed to be abating, just when I was longing for someone to take on Ibsen instead, an unmissable occasion presents itself. Anya Reiss, whose acerbic Spur of the Moment was staged as she was finishing her A-levels, has written a new version of The Seagull, which transplants the action to somewhere "like the Isle of Man" in the 21st century. There are B&Bs and mobiles; the desperate young writer Konstantin destroys his work by tipping water into his laptop. The result is less wild than Benedict Andrews's production of Three Sisters, less freewheelingly absurd than Vakhtangov's production of Uncle Vanya, but – in Russell Bolam's sly and absorbing production – absolutely as transporting. It is the opposite of "museum theatre", which is one of the play's targets. It is not at all pretentious, which is another target.

Chekhov did an extraordinary thing in making the static life of a writer dramatic, examining loneliness and failure alongside self-aggrandisement and celebrity. He moves seamlessly from murmur to momentousness. So does this production, performed against rough brick, with trains rumbling like thunder and actors trickling, talking, down the aisles through the audience: Nina has to be dragged on. An inspired minimalism in the tricky last scene, in which Nina has to flap on as a gull, shows desolate Konstantin looking at the world outside – a chandelier and spectral figures – through gauze.

It is contemporary – Emily Dobbs's Masha, who always wears black, is a sulky goth, in big boots, torn tights and a sneer – but holds in mind that the contemporary contains the past. Malcolm Tierney's Sorin is a miracle of snoozy, contemplative fading. Anthony Howell's Trigorin, the destructive celebrity author, is unusually convincing: not a swaggerer or a smirker but a lethally hesitant presence. You would think that was it for Chekhov, but next year one of the most luminous of young directors, Blanche McIntyre, is also directing The Seagull for Headlong. So yet again audiences will have to make a date with this 1895 play.

At the Gate, updating is more obtrusive. It is cheeky of them to advertise The Trojan Women as featuring Tamsin Greig and Roger Lloyd Pack, when these actors put in only brief video appearances, glimmering as Athena and Poseidon, full of condescension, irony and sophistication, tinged in Greig's case with an entertaining lubriciousness. Still, it is one of the smart aspects of Christopher Haydon's production that it pitches the gods in a virtual medium against the bawling fleshy horrors on stage.

Caroline Bird's ripe, sometimes overwritten version of Euripides's drama puts the conquered – and raped and widowed – women of Troy in a terrible 21st-century prison hospital, where Hecuba (impressive, crisp Dearbhla Molloy) queens it over her fellow inmates with her false memories of an idyllic Troy, while Louise Brealey – nimbly but without any obvious point – triples up as Cassandra, Andromache and Helen. Flames beat against the window, while Talthybius puzzles over a crossword clue: is it "machete" or "cleaver"?

The unremittingly intense evening has two flashes of illumination. It is powerful to have as the chorus a single pregnant woman – performed with terrific flailing anger and desperation by Lucy Ellinson. It is ingenious to describe such a woman, smuggling a rebel in her belly, as a Trojan horses. Well, nags.